Transition temperature of the weakly interacting Bose gas: perturbative solution of the crossover equations in the canonical ensemble

Citation
M. Wilkens et al., Transition temperature of the weakly interacting Bose gas: perturbative solution of the crossover equations in the canonical ensemble, J PHYS B, 33(20), 2000, pp. L779-L786
Citations number
25
Categorie Soggetti
Physics
Journal title
JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS
ISSN journal
09534075 → ACNP
Volume
33
Issue
20
Year of publication
2000
Pages
L779 - L786
Database
ISI
SICI code
0953-4075(20001028)33:20<L779:TTOTWI>2.0.ZU;2-9
Abstract
We compute the shift of the critical temperature T-c with respect to the id eal case for a weakly interacting uniform Bose gas. We work in the framewor k of the canonical ensemble, extending the criterion of condensation provid ed by the canonical particle counting statistics for the zero-momentum stat e of the uniform ideal gas. The perturbative solution of the crossover equa tion to lowest order in powers of the scattering length yields (T-c - T-c(0 ))/T-c(0) = -0.93a rho (1/3), where T-c(0) is the transition temperature of the corresponding ideal Bose gas, a is the scattering length, and rho is t he particle number density. This result is at variance with the standard gr and canonical prediction of a null shift of the critical temperature in the lowest perturbative order. The non-equivalence of statistical ensembles fo r the ideal Bose gas is thus confirmed (at the lowest perturbative level) a lso in the presence of interactions.